Optimal fineness ratio for minimum drag in large whales

The optimum fineness ratio (X = L/d, where L and d are body length and profile height, respectively) for minimum drag is about 4.5 and many fast swimming fish are characterized by values of this order. However, values for large whales that undergo extensive migrations (e.g., Balaenopteridae, Balaenidae, and Physeteridae) are as high as 8. A plot of fineness ratio versus mass (M) for different species of large whales shows that the optimal fineness ratio for minimum drag and therefore the minimum cost of transport increases slowly with increasing mass (X = 4M 0.06 ). Optimal fineness ratio was determined from a simple hydromechanical model based on the sum of friction and pressure drag on an equivalent cylindrical body, which indicate a small positive dependence (0.11) of optimal fineness ratio for minimum drag with increasing body mass, suggesting an adaptation for reducing the energy cost of swimming.